The first and last term of a linear sequence (AP) are 6 and 10 respectively. If the sum of the sequence is 40. Find the number of terms
A.
nth = 3
B.
nth = 4
C.
nth = 5
D.
nth = 6
Correct Answer: nth = 5
Explanation
nth term of a linear sequence (AP) = a+(n − 1)d
first term = 6, last term = 10 sum − 40
i.e. a = 6, l = 10, S = 40
Sn
= n/2(2a + (n − 1)d or Sn = ÷2 (a + l)
Sn
= n/2(a + l)
40 = n/2(6 + 10)
40 = 8n
8n = 40
8n = 40
n = 40/8
= 5
The number of terms = 5
nth term of a linear sequence (AP) = a+(n − 1)d
first term = 6, last term = 10 sum − 40
i.e. a = 6, l = 10, S = 40
Sn
= n/2(2a + (n − 1)d or Sn = ÷2 (a + l)
Sn
= n/2(a + l)
40 = n/2(6 + 10)
40 = 8n
8n = 40
8n = 40
n = 40/8
= 5
The number of terms = 5
